There is a lock on the part that attaches to the frame, but it's fairly simple and I wouldn't rely on it if I was leaving the bike for any length of time. You can see the lock in the product video.
I use the rack for my bike with 26 inch wheels and "usual" bike tyres 2.25 inch wide.
27.5 inch or 29 inch wheels will certainly also fit. A bike with normal bike tyres can be mounted well on the carrier, but I would not mount bikes with balloon tyres "fatbikes".